# Find the differential dy for the given values of x and dx. y=frac{e^x}{10},x=0,dx=0.1

Find the differential dy for the given values of x and dx. $y=\frac{{e}^{x}}{10},x=0,dx=0.1$
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Aniqa O'Neill
$y={e}^{\frac{x}{10}}$
Differentiate both sides with respect to x
$\frac{dy}{dx}=\frac{d\left({e}^{\frac{x}{10}}\right)}{dx}$
Using chain rule, we can write
$\frac{dy}{dx}=\frac{d\left({e}^{\frac{x}{10}}\right)}{d\left(\frac{x}{10}\right)}\cdot \frac{d\left(\frac{x}{10}\right)}{dx}$
Recall: $\frac{d\left({e}^{u}\right)}{du}={e}^{u}$
$\frac{dy}{dx}={e}^{\frac{x}{10}}\cdot \frac{1}{10}$
$\frac{dy}{dx}=\frac{{e}^{\frac{x}{10}}}{10}$
Multiply both sides by dx
$dy=\frac{{e}^{\frac{x}{10}}}{10dx}$
Result: $dy=\frac{{e}^{\frac{x}{10}}}{10dx}$